It's a fighter-bomber, just like the Su-7, Su-17 Fitter, Su-24 Fencer. So F is correct. It's of course strange, but the B is reserved for the real strategic bombers, not frontline tactical (fighter)bombers. It's like calling a Tornado GR.4 a bomber, it is, but would you call it that? Don't forget the Su-34 still carries AAMs, including R-77 AMRAAMski, which gives it better AA capability than most western fighter-bombers/strikers. Let's see, in a conflict, I would call Backfire over the radio, you know it's a bomber of good size, which has no defensive weapons, but probably fighter escorts, and it's on its way to attack your carrier. But when two Su-34s are coming in, it means they have A-A weapons as well, are agile and fast, it's likely they are on a bombing mission, but it would make more sense to call them out as fighters than bombers, right?
Anyway, designation systems never make total sense! It's impossible to classify so many designs. Especially when it's either F or B.